Marksmen typically train and hone their shooting skills by engaging in skeet, trap or sporting clay shooting at a shooting range. The objective for a marksman is to successfully hit a moving target by tracking at various distances and angles and anticipating the delay time between the shot and the impact. In order to hit the moving target, the marksman must aim the weapon ahead of and above the moving target by a distance sufficient to allow a projectile fired from the weapon sufficient time to reach the moving target. The process of aiming the weapon ahead of the moving target is known in the art as “leading the target.” “Lead” is defined as the distance between the moving target and the aiming point. The correct lead distance is critical to successfully hit the moving target. Further, the correct lead distance is increasingly important as the distance of the marksman to the moving target increases, the speed of the moving target increases, and the direction of movement becomes more oblique.
Trap shooting range 200 comprises firing lanes 201 and trap house 202. Stations 203, 204, 205, 206, and 207 are positioned along radius 214 from center 218 of trap house 202. Radius 214 is distance 216 from center 218. Distance 216 is 48 feet. Each of stations 203, 204, 205, 206, and 207 is positioned at radius 214 at equal arc lengths. Arc length 213 is 9 feet. Stations 208, 209, 210, 211, and 212 are positioned along radius 215 from center 218. Radius 215 is distance 217 from center 218. Distance 217 is 81 feet. Each of stations 208, 209, 210, 211, and 212 is positioned at radius 215 at equal arc lengths. Arc length 227 is 12 feet. Field 226 has length 221 from center 218 along center line 220 of trap house 202 to point 219. Length 221 is 150 feet. Boundary line 222 extends 150 feet from center 218 at angle 224 from center line 220. Boundary line 223 extends 150 feet from center 218 at angle 225 from center line 220. Angles 224 and 225 are each 22° from center line 220. Trap house 202 launches clay targets at various trajectories within field 226. Marksman 228 positioned at any of stations 203, 204, 205, 206, 207, 208, 209, 210, 211, and 212 attempts to shoot and break the launched clay targets.
FIGS. 3A, 3B, 3C, and 3D depict examples of target paths and associated projectile paths illustrating the wide range of lead distances and distances required of the marksman. The term “projectile,” as used in this application, means any projectile fired from a weapon but more typically a shotgun round comprised of pellets of various sizes. For example, FIG. 3A shows a left to right trajectory 303 of target 301 and left to right intercept trajectory 304 for projectile 302. In this example, the intercept path is oblique, requiring the lead to be a greater distance along the positive X axis. FIG. 3B shows a left to right trajectory 307 of target 305 and intercept trajectory 308 for projectile 306. In this example, the intercept path is acute, requiring the lead to be a lesser distance in the positive X direction. FIG. 3C shows a right to left trajectory 311 of target 309 and intercepting trajectory 312 for projectile 310. In this example, the intercept path is oblique and requires a greater lead in the negative X direction. FIG. 3D shows a proximal to distal and right to left trajectory 315 of target 313 and intercept trajectory 316 for projectile 314. In this example, the intercept path is acute and requires a lesser lead in the negative X direction.
FIGS. 4A and 4B depict a range of paths of a clay target and an associated intercept projectile. The most typical projectile used in skeet and trap shooting is a shotgun round, such as a 12-gauge round or a 20 gauge round. When fired, the pellets of the round spread out into a “shot string” having a generally circular cross-section. The cross-section increases as the flight time of the pellets increases. Referring to FIG. 4A, clay target 401 moves along path 402. Shot string 403 intercepts clay target 401. Path 402 is an ideal path, in that no variables are considered that may alter path 402 of clay target 401 once clay target 401 is launched.
Referring to FIG. 4B, path range 404 depicts a range of potential flight paths for a clay target after being released on a shooting range. The flight path of the clay target is affected by several variables. Variables include mass, wind, drag, lift force, altitude, humidity, and temperature, resulting in a range of probable flight paths, path range 404. Path range 404 has upper limit 405 and lower limit 406. Path range 404 from launch angle θ is extrapolated using:
                    x        =                              x            o                    +                                    v              xo                        ⁢            t                    +                                    1              2                        ⁢                          a              x                        ⁢                          t              2                                +                      C            x                                              Eq        .                                  ⁢        1                                y        =                              y            o                    +                                    v              yo                        ⁢            t                    +                                    1              2                        ⁢                          a              y                        ⁢                          t              2                                +                      C            y                                              Eq        .                                  ⁢        2            where x is the clay position along the x-axis, xo is the initial position of the clay target along the x-axis, vxo is the initial velocity along the x-axis, ax is the acceleration along the x-axis, t is time, and Cx is the drag and lift variable along the x-axis, y is the clay position along the y-axis, yo is the initial position of the clay target along the y-axis, vyo is the initial velocity along the y-axis, ay is the acceleration along the y-axis, t is time, and Cy is the drag and lift variable along the x-axis. Upper limit 405 is a maximum distance along the x-axis with Cx at a maximum and a maximum along the y-axis with Cy at a maximum. Lower limit 406 is a minimum distance along the x-axis with Cx at a minimum and a minimum along the y-axis with Cy at a minimum. Drag and lift are given by:
                              F          drag                =                              1            2                    ⁢          ρ          ⁢                                          ⁢                      v            2                    ⁢                      C            D                    ⁢          A                                    Eq        .                                  ⁢        3            where Fdrag is the drag force, ρ is the density of the air, v is vo, A is the cross-sectional area, and CD is the drag coefficient;
                              F          lift                =                              1            2                    ⁢          ρ          ⁢                                          ⁢                      v            2                    ⁢                      C            L                    ⁢          A                                    Eq        .                                  ⁢        4            where Flift is the lift force, ρ is the density of the air, v is vo, A is the planform area, and CL is the lift coefficient.
Referring to FIG. 5, an example of lead from the perspective of the marksman is described. Marksman 501 aims weapon 502 at clay target 503 moving along path 504 left to right. In order to hit clay target 503, marksman 501 must anticipate the time delay for a projectile fired from weapon 502 to intercept clay target 503 by aiming weapon 502 ahead of clay target 503 at aim point 505. Aim point 505 is lead distance 506 ahead of clay target 503 along path 504. Marksman 501 must anticipate and adjust aim point 505 according to a best guess at the anticipated path of the target.
Clay target 503 has initial trajectory angles γ and β, positional coordinates x1, y1 and a velocity v1. Aim point 505 has coordinates x2, y2. Lead distance 506 has x-component 507 and y-component 508. X-component 507 and y-component 508 are calculated by:Δx=x2−x1   Eq. 5Δy=y2−y1   Eq. 6where Δx is x component 507 and Δy is y component 508. As γ increases, Δy must increase. As γ increases, Δx must increase. As β increases, Δy must increase.
The prior art has attempted to address the problems of teaching proper lead distance with limited success. For example, U.S. Pat. No. 3,748,751 to Breglia, et al. discloses a laser, automatic fire weapon simulator. The simulator includes a display screen, a projector for projecting a motion picture on the display screen. A housing attaches to the barrel of the weapon. A camera with a narrow band-pass filter positioned to view the display screen detects and records the laser light and the target shown on the display screen. However, the simulator requires the marksman to aim at an invisible object, thereby making the learning process of leading a target difficult and time-consuming.
U.S. Pat. No. 3,940,204 to Yokoi discloses a clay shooting simulation system. The system includes a screen, a first projector providing a visible mark on the screen, a second projector providing an infrared mark on the screen, a mirror adapted to reflect the visible mark and the infrared mark to the screen, and a mechanical apparatus for moving the mirror in three dimensions to move the two marks on the screen such that the infrared mark leads the visible mark to simulate a lead-sighting point in actual clay shooting. A light receiver receives the reflected infrared light. However, the system in Yokoi requires a complex mechanical device to project and move the target on the screen, which leads to frequent failure and increased maintenance.
U.S. Pat. No. 3,945,133 to Mohon, et al. discloses a weapons training simulator utilizing polarized light. The simulator includes a screen and a projector projecting a two-layer film. The two-layer film is formed of a normal film and a polarized film. The normal film shows a background scene with a target with non-polarized light. The polarized film shows a leading target with polarized light. The polarized film is layered on top of the normal non-polarized film. A polarized light sensor is mounted on the barrel of a gun. However, the weapons training simulator requires two cameras and two types of film to produce the two-layered film making the simulator expensive and time-consuming to build and operate.
U.S. Pat. No. 5,194,006 to Zaenglein, Jr. discloses a shooting simulator. The simulator includes a screen, a projector for displaying a moving target image on the screen, and a weapon connected to the projector. When a marksman pulls the trigger a beam of infrared light is emitted from the weapon. A delay is introduced between the time the trigger is pulled and the beam is emitted. An infrared light sensor detects the beam of infrared light. However, the training device in Zaenglein, Jr. requires the marksman to aim at an invisible object, thereby making the learning process of leading a target difficult and time-consuming.
U.S. Patent Publication No. 2010/0201620 to Sargent discloses a firearm training system for moving targets. The system includes a firearm, two cameras mounted on the firearm, a processor, and a display. The two cameras capture a set of stereo images of the moving target along the moving target's path when the trigger is pulled. However, the system requires the marksman to aim at an invisible object, thereby making the learning process of leading a target difficult and time-consuming. Further, the system requires two cameras mounted on the firearm making the firearm heavy and difficult to manipulate leading to inaccurate aiming and firing by the marksman when firing live ammunition without the mounted cameras.
The prior art fails to disclose or suggest a system and method for simulating a lead for a moving target using generated images of targets projected at the same scale as viewed in the field and a phantom target positioned ahead of the targets having a variable contrast. The prior art further fails to disclose or suggest a system and method for simulating lead in a virtual reality system. Therefore, there is a need in the art for a shooting simulator that recreates moving targets at the same visual scale as seen in the field with a phantom target to teach proper lead of a moving target in a virtual reality platform.